Evolution of distorted rotating black holes. III. Initial data

We evolve equal-mass, equal-spin black-hole binaries with specific spins of a/mH ∼ 0.925, the highest spins simulated thus far and nearly the largest possible for Bowen-York black holes, in a set of configurations with the spins counter-aligned and pointing in the orbital plane, which maximizes the recoil velocities of the merger remnant, as well as a configuration where the two spins point in the same direction as the orbital angular momentum, which maximizes the orbital hang-up effect and remnant spin. The coordinate radii of the individual apparent horizons in these cases are very small and the simulations require very high central resolutions (h ∼ M/320). We find that these highly spinning holes reach a maximum recoil velocity of ∼ 3300 km s −1 (the largest simulated so far) and, for the hangup configuration, a remnant spin of a/mH ∼ 0.922. These results are consistent with our previous predictions for the maximum recoil velocity of ∼ 4000 km s −1 and remnant spin; the latter reinforcing the prediction that cosmic censorship is not violated by merging highlyspinning black-hole binaries. We also numerically solve the initial data for, and evolve, a single maximal-Bowen-York-spin black hole, and confirm that the 3-metric has an O(r −2 ) singularity at the puncture, rather than the usual O(r −4 ) singularity seen for non-maximal spins.

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“…For completeness, we reproduce this calculation and adapt it to our setting. We use the coordinate transformation [66] r =r 1 + m + a 2r…”

Section: A Maximum Spin Bowen-york Initial Datamentioning

confidence: 99%

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

2008

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“…Furthermore, even with this gauge choice, if the code is run with too high a resolution, axis instabilities are again encountered, and these instabilities eventually crash the code at late times. Similar problems with axis instabilities have been encountered in the case of rotating [6,43,40,41] and colliding black holes [44,4,45,46,7,42,47].…”

Section: Rmentioning

confidence: 89%

Symmetry Without Symmetry: Numerical Simulation of Axisymmetric Systems Using Cartesian Grids

Alcubierre

Brandt

Brügmann

et al. 2001

Int. J. Mod. Phys. D

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151

188

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We present a new technique for the numerical simulation of axisymmetric systems. This technique avoids the coordinate singularities which often arise when cylindrical or polar-spherical coordinate finite difference grids are used, particularly in simulating tensor partial differential equations like those of 3 + 1 numerical relativity. For a system axisymmetric about the z axis, the basic idea is to use a 3-dimensional Cartesian (x, y, z) coordinate grid which covers (say) the y = 0 plane, but is only one finite-difference-molecule-width thick in the y direction. The field variables in the central y = 0 grid plane can be updated using normal (x, y, z)-coordinate finite differencing, while those in the y = 0 grid planes can be computed from those in the central plane by using the axisymmetry assumption and interpolation. We demonstrate the effectiveness of the approach on a set of fully nonlinear test computations in 3 + 1 numerical general relativity, involving both black holes and collapsing gravitational waves.

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“…This construction is based on the form of the Kerr metric in quasi-isotropic coordinates [11], and following the suggestions outlined in [44,45] extends the work in axisymmetry of [46].…”

Section: Discussionmentioning

confidence: 99%

Beyond the Bowen–York extrinsic curvature for spinning black holes

Hannam¹,

Husa²,

Bruegmann³

et al. 2007

Class. Quantum Grav.

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Abstract. It is well-known that Bowen-York initial data contain spurious radiation. Although this "junk" radiation has been seen to be small for non-spinning black-hole binaries in circular orbit, its magnitude increases when the black holes are given spin. It is possible to reduce the spurious radiation by applying the puncture approach to multiple Kerr black holes, as we demonstrate for examples of head-on collisions of equal-mass black-hole binaries.

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Evolution of distorted rotating black holes. III. Initial data

Cited by 67 publications

References 31 publications

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

Extra-large remnant recoil velocities and spins from near-extremal-Bowen-York-spin black-hole binaries

Symmetry Without Symmetry: Numerical Simulation of Axisymmetric Systems Using Cartesian Grids

Beyond the Bowen–York extrinsic curvature for spinning black holes

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